In a small bowl, combine water, sugar, and instant yeast. Stir until the yeast and sugar have dissolved. Let it sit for about five minutes until the mixture becomes frothy.
Meanwhile, combine all-purpose flour, semolina flour, and salt in a large mixing bowl or a stand mixer. Mix well.
Pour the yeast mixture into the dry ingredients. Mix everything together until a sticky dough forms. If kneading by hand, transfer the dough onto a clean, lightly floured surface. Knead the dough for five to seven minutes until it becomes smooth and elastic. If the dough feels too sticky, you can add a little more all-purpose flour. If kneading in a mixer, mix with the dough hook attachment for four minutes on low speed.
Shape the dough into a ball and cover it with a clean kitchen towel. Let it rest for an hour to allow the dough to rest, rise, and become smoother and more pliable.
Once the dough has rested, divide it into small pieces, each about the size of a golf ball.
Take one piece of dough and flatten it with your hands. Using a lightly oiled rolling pin, roll it into a thin, rectangular shape on an oiled work surface.
Place small ¼ teaspoon dollops of room temperature vegan butter evenly over the surface of the rolled-out dough. Sprinkle lightly with about 1 teaspoon of semolina flour.
Starting from one end, fold the dough into thirds, similar to folding a letter.
Rotate the folded dough 90 degrees and roll it out again into a thin rectangular shape.
Dollop again with vegan butter, dust with semolina, and repeat folding to form a thicker square shape.
Repeat steps 6-10 with the remaining portions of dough.
Brush the surface of the rolled-out dough with olive oil, and gently roll it into a thinner, wider square, about 5 inches (12.5 cm) on each side.
Heat a non-stick skillet or griddle over medium heat.
Place the folded msemen onto the heated skillet and cook for a few minutes on each side until golden brown and cooked through.
Remove the cooked msemen from the skillet and place it on a plate lined with paper towels to absorb any excess oil.
Repeat the process with the remaining dough pieces, adding more oil to the skillet as needed.